11 July 2023 07:25:55 AM

triangle_witherden_rule_test():
  C++ version
  Test triangle_witherden_rule().

triangle_witherden_rule_test01():
  Quadrature rule for the triangle,
  given in barycentric coordinates.
  Precision p = 5

  Number of nodes N = 7

     I      W          A           B           C

     0       0.225    0.333333    0.333333    0.333333
     1    0.125939    0.101287    0.797427    0.101287
     2    0.125939    0.797427    0.101287    0.101287
     3    0.125939    0.101287    0.101287    0.797427
     4    0.132394    0.470142   0.0597159    0.470142
     5    0.132394   0.0597159    0.470142    0.470142
     6    0.132394    0.470142    0.470142   0.0597159

  Weight Sum = 1

triangle_witherden_rule_test02():
  Test the precision of a quadrature rule for the unit triangle.

  Number of nodes N = 7

  Stated precision of rule    = 5
  Number of quadrature points = 7

  Degree  Maximum error

   0               5.55112e-17
   1                         0
   2               1.38778e-17
   3               6.93889e-18
   4               6.93889e-18
   5               8.67362e-19
   6               8.18846e-05
   7               0.000254052

triangle_witherden_rule_test03():
  Test the precision of quadrature rules for the unit triangle.
  Check rules of precision p = 0 through 20
  for error in approximating integrals of monomials.

              maximum                   maximum
   p          absolute                  relative
              error                     error

   0                         0                         0
   1               5.55112e-17               3.33067e-16
   2               2.77556e-17               1.66533e-16
   3               1.11022e-16               3.33067e-16
   4               1.11022e-16               4.16334e-16
   5               5.55112e-17               3.64292e-16
   6               5.55112e-17               4.16334e-16
   7               2.77556e-17                 6.245e-16
   8               5.55112e-17                 6.245e-16
   9               1.66533e-16               1.14492e-15
  10               2.22045e-16               1.14492e-15
  11               4.44089e-16                1.5027e-15
  12               4.44089e-16               2.84148e-15
  13               4.44089e-16               2.70617e-15
  14               6.93889e-17                3.1225e-15
  15               6.93889e-17               2.28928e-15
  16               3.33067e-16               9.15674e-15
  17               2.77556e-17                2.1233e-15
  18               4.44089e-16               3.85629e-15
  19               2.77556e-16                6.7394e-15
  20               1.11022e-16               7.21298e-15

triangle_witherden_rule_test()
  Normal end of execution.

11 July 2023 07:25:55 AM